Is a large number of RSA-encrypted files a vulnerability?

Question

Would having a large number (10^4) of RSA encrypted files make it easier for an attacker to find my private RSA key?

Update: These files would be available to the attacker, and perhaps the content of a few of them could be guessed. The GnuPG implementation with a 2048-bit RSA key would be used, and the public key would be public.

Answer 1

Short answer: there is no issue in encrypting 10⁴ files with the same key.

Longer answer: it is called public encryption for a reason: the public key is, well, public. This means that anybody can encrypt data with the public key (it is the decrypting part which is reserved for the private key owner). In particular, the attacker can encrypt millions of files with your public key, if he wishes so. Asymmetric encryption systems are specifically designed to not suffer from that. In the case of RSA, this implies that any decent RSA encryption protocol includes random padding bytes, as PKCS#1 describes; the protocol used by GnuPG to encrypt data is decent.

Answer 2

No. As long as you're using 2048 RSA and padding, and your public key passphrase is long (I like 20+ characters), uses alphanumerical and special characters, you shouldn't have any problem. Just make sure your private key isn't compromised :)